Video: Finding an Unknown Element Using an Equality of Sets

If {3, 5, 1} = {1, 3, 𝑥}, what is the value of 𝑥?

01:15

Video Transcript

If the set including elements three, five, and one is equal to the set of elements one, three, and 𝑥, what is the value of 𝑥?

Now it may seem like the first numbers go together, the second numbers go together, and the third numbers go together. But that is not right, not correct, and here’s why. when we have a set, the order that we write the elements actually doesn’t matter. So if we wanted to, we could write instead of three, five, one, we could write five, three, one or one, three, five. It doesn’t matter.

So let’s compare the sets. This first set let’s call it A, and the second set we will call B. So set A has numbers three, five, and one. Set B has numbers one, three, and 𝑥. So let’s see what matches up, because if the sets are equal, they should have the exact same elements in them. So A and B both have element three. They both have element one. And all that’s left that has to match is five and 𝑥. Therefore, 𝑥 must be equal to five.

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